{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Attention on MNIST (Saliency and grad-CAM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets build the mnist model and train it for 5 epochs. It should get to about ~99% test accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "60000 train samples\n",
      "10000 test samples\n",
      "WARNING:tensorflow:From C:\\Users\\tkramer\\AppData\\Local\\Continuum\\miniconda3\\envs\\donkey\\lib\\site-packages\\tensorflow\\python\\ops\\resource_variable_ops.py:435: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n",
      "WARNING:tensorflow:From C:\\Users\\tkramer\\AppData\\Local\\Continuum\\miniconda3\\envs\\donkey\\lib\\site-packages\\tensorflow\\python\\keras\\layers\\core.py:143: calling dropout (from tensorflow.python.ops.nn_ops) with keep_prob is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use `rate` instead of `keep_prob`. Rate should be set to `rate = 1 - keep_prob`.\n",
      "Train on 60000 samples, validate on 10000 samples\n",
      "WARNING:tensorflow:From C:\\Users\\tkramer\\AppData\\Local\\Continuum\\miniconda3\\envs\\donkey\\lib\\site-packages\\tensorflow\\python\\ops\\math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.cast instead.\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 6s 103us/sample - loss: 0.2390 - acc: 0.9280 - val_loss: 0.0533 - val_acc: 0.9816\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 4s 62us/sample - loss: 0.0823 - acc: 0.9752 - val_loss: 0.0384 - val_acc: 0.9862\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 4s 64us/sample - loss: 0.0621 - acc: 0.9807 - val_loss: 0.0326 - val_acc: 0.9889\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 4s 63us/sample - loss: 0.0500 - acc: 0.9846 - val_loss: 0.0320 - val_acc: 0.9891\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 4s 62us/sample - loss: 0.0434 - acc: 0.9860 - val_loss: 0.0310 - val_acc: 0.9892\n",
      "Test loss: 0.030951254331048405\n",
      "Test accuracy: 0.9892\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import numpy as np\n",
    "import tensorflow.python.keras as keras\n",
    "\n",
    "from tensorflow.python.keras.datasets import mnist\n",
    "from tensorflow.python.keras.models import Sequential, Model\n",
    "from tensorflow.python.keras.layers import Dense, Dropout, Flatten, Activation, Input\n",
    "from tensorflow.python.keras.layers import Conv2D, MaxPooling2D\n",
    "from tensorflow.python.keras import backend as K\n",
    "\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 5\n",
    "\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "\n",
    "# the data, shuffled and split between train and test sets\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')\n",
    "\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = keras.utils.to_categorical(y_test, num_classes)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax', name='preds'))\n",
    "\n",
    "model.compile(loss=keras.losses.categorical_crossentropy,\n",
    "              optimizer=keras.optimizers.Adam(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=1,\n",
    "          validation_data=(x_test, y_test))\n",
    "\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saliency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize activation over final dense layer outputs, we need to switch the `softmax` activation out for `linear` since gradient of output node will depend on all the other node activations. Doing this in keras is tricky, so we provide `utils.apply_modifications` to modify network parameters and rebuild the graph.\n",
    "\n",
    "If this swapping is not done, the results might be suboptimal. We will start by swapping out 'softmax' for 'linear' and compare what happens if we dont do this at the end."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets pick an input over which we want to show the attention."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x28e75c0ce48>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "class_idx = 0\n",
    "indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "\n",
    "# pick some random input from here.\n",
    "idx = indices[0]\n",
    "\n",
    "# Lets sanity check the picked image.\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (18, 6)\n",
    "\n",
    "plt.imshow(x_test[idx][..., 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time for saliency visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x290b73329e8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_saliency\n",
    "from vis.utils import utils\n",
    "from tensorflow.python.keras import activations\n",
    "\n",
    "# Utility to search for layer index by name. \n",
    "# Alternatively we can specify this as -1 since it corresponds to the last layer.\n",
    "layer_idx = utils.find_layer_idx(model, 'preds')\n",
    "\n",
    "# Swap softmax with linear\n",
    "model.layers[layer_idx].activation = activations.linear\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx])\n",
    "# Plot with 'jet' colormap to visualize as a heatmap.\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To used guided saliency, we need to set `backprop_modifier='guided'`. For rectified saliency or deconv saliency, use `backprop_modifier='relu'`. Lets try these options quickly and see how they compare to vanilla saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for modifier in ['guided', 'relu']:\n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx,\n",
    "                               seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "    plt.figure()\n",
    "    plt.title(modifier)\n",
    "    plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both of them look a lot better than vanilla saliency! This in inline with observation in the paper.\n",
    "\n",
    "We can also visualize negative gradients to see the parts of the image that contribute negatively to the output by using `grad_modifier='negate'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x290f286fc50>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx], \n",
    "                           backprop_modifier='guided', grad_modifier='negate')\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets try all the classes and show original inputs and their heatmaps side by side. We cannot overlay the heatmap on original image since its grayscale.\n",
    "\n",
    "We will also compare the outputs of guided and rectified or deconv saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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o3uP1D6P8ltvt7HnuxtAOl93gDOjU9O6YfGOUfxVfBwDcg/B5zKJh/6uwsl8i/Mq+bbNsOXCV/17yElyeaR6aVEbg5QBG1iibAmCRMWYAgEXufyUNjkI/fJVbq0XlmxEGI2l9tUVlmxFUtvlAvR24MeavqD20GY3gof4okqM5KA3gcOmBNmhbs1jlmxH6ISZOiMo2I6hs84F0jZi9jDGbAMAYs0lEetZ3QSboOPs1l9Y+Vlc06wd7lwIA7vxGSTh3sTUi3F3aP+aKQNHnB8OzV2+K8kf8dQ4AYFBb8jdPHGrHlQaTIfnylNe/67JQRCv0fn7/7TZTTpeMt9O/UY88E3v3M89xBlu2J/rrybA54c7f0Qk/c+nboWjacVH2vHZ2L9wXHjsvKtsx26nHJtLqzBlhapwcDKtestR2vaxp+ltMxqzr3CyrlC7pb9/h3C89GxV1ICOzPOPe8XyKMObVBOTPL/NCO42m4iXXhKJEMKzfMnUaAKDf5HVR2Qa/GrA4GOySdqIBqXUOTZqypZWY1S4tDZ/1+2L9vNE9rEc4a2tYHbz4KacgGMvrBNznsTy8+9ZBQWUoa6xaBo9Qz+HnCxPDu99SMS0cdxrX+a+wQoJUkpPc/UvocOIhl+ExMMf79qqgC6gs9WBWWfdCEZEJACYAQHt0qOdspSGwbIEuTVqX5ojKN3skyzYn479mSbpeKB+LyJEA4NItdZ1ojJlpjBlijBnShn2olEORknxZttAfx1RJq+2qfFMiTdkeajco5VCkOwJ/HsAVAKa69LmM1SjDHNhsfYQ7zgm+wl+4tOPsT2KuiOfjq8+I8l9pa8U27dMTorKSR963z0u3oslkQb7eyk3+wdU0TZ7kVZfkr/pGAgAwrzwsQQ4qTiAEP6KNjsf7WMekvhlHU/OFbhq8mablZOq66Yc/BQA88ca/0nPcNJODNiXVw9c5JX/wLLVd78dcEYqqyPNgqmsZU3n6bD0Q5uOfQhF5QESNieO2eycglsWs4IF1ylVWHdLOx7YGsEy+Fs51WukNN7Cft6OE8mt482rfwdYbQCxN2RYheGN4n++KcHjUNajJYvl6+KfcpWPovOi7Te1kTVC7RAsWyA7bZoz1v95/37GhkIOCeee26fRjPoPCQPjeNHEXXTTepfOpLM7Dh9WAdf7u1SIVN8InYDV33UWkEjYy/VQAT4vIVQA+BHBxyk9UknjTvIbPsBX7sRcvmz8D1vVf5ZsR5sB6s+0BcA+gss0gNWXbClDZ5px6O3BjzGV1HDo7w3XJO4r6Bf/m6T+eHuXbSGsAwDP3h41Xj9i0JK1nDJLTk/5faGZvM8Z8gozL1/+q8xyBV3zF+fp6g9wfqIw3m3WjppNos9iES8kHOskX4TE3whpOMwHacGbobjfEHPpQKBzmAgbxJj6xO9LwVHwnaq/quy1LsuX6sK86572s2djt601fw83dYo6Tz3vkLkyjwCfDSH/jF7bNflpEeuWp4ZkjTrCD4hfvo7qN+b5Nk5wDeETon5+gspqynQljtqcp270IhlLv305tat49Np0a/K9xI33WpW4mOYZGztEOx1eEov40bVnv2ldxCEa1f5a75zoKq3tiTNu+7h56Dn02fUtdhtvm8y7l8LwczCoRc7xnTFk8uhJTURSlQNEOXFEUpUApqGBWuWbdDWGq87V2wVD01j47Rer2t9Tj9jY93t+UDX1xRj9WqyRcyv7yMYGNupN/9hrvnx2mf+deFAxq84ucwa6Erief7qriJ1zu0nD8lTkx9WRjYOrBf7LH/hppfedxntUqnPfqBHa099NzUr31DyqUT6f5ZeXhcNlVIfBT2cXewEZG5Nleh8VGSlZHJZBdeFNj3754dyD3zlPYOMhycn7ss1l14QPN0Tsl2PJr20+PyWF5/dZBx9SoA/DltcGXf+0vXR3LSZWzhuq0wKs+KEZ4pELhRU8cDCuu7aa+25SOwBVFUQoUHYHHsPd863a1cgyFmiQf9u/94AcAgMNeXYaWARvj2LDiRjwVMSv17vx+lL0N/xLlB+23xrG7v/yTcO68mNCoJeSC190ZzJazKxbPBPy5TbkjT6bg0VfcaN6P5E6LSrqcFHzddkyxfohXvBSMwK/xaH12hcvwV7+uYGCejK4yjuFzhBWNW6jM42dbPHKlWWGxMzRW8YzYr2akmdoBHu1+BwCw9Qyaaazx7TjMvLuCwu66vVuvejM4NPzmDApru7TMZUrpOT7YFa+uZAOx/zx5RunfXY2YiqIozRbtwBVFUQoUVaHE8OG59netWILa5LIPgj9ohwV2g1qDlkKc4Q0IU2vyay216o4eNwXj0GmX0ZSxxKW0u0qbkWFqu7/MqV4SPw0nJOI2LWZ/aT/9ztamu9mmvnqzCsPJemgdO/IstHKrQtgtav71tNIT3iDMO8SwLD2f15HPBoLwjl41FBfQ6R8p/3TIVvn6seHVq43qUEN0dz7jS7nQyeHC70QlY1yscwBYMv5bAIDZe2lH6KXUTruW2XQ7G91vcyl/hrwKttSl/L71q048OgJXFEUpULQDVxRFKVBUheJo1SlYgS8/0/rF7jwYAmZv+VmIWd1u7+u5q1he46f+tKzaxQHfaoPSWXj1/RsuLae7jKuIuedEKvMeJ+yFwh4TzbUZ+2k3eyi46Es0i98xiiJgXW2Dhc35b7pkOi/99uoS9qCKm7LnUh3VCsEbw6sSTqbjrs7tKSha9SV03MtpfkwZ+1+TKmibV4CGNQoYVmrTaUE5evveW8PxkTYMxI4p7E9ObW+7i/VQShGyKnw75S3VWLZe9umprHQEriiKUqA016FLg3m37CtRfl73/wIAjH43jCzbvdCSR91sHOLRgV89Rys6B/uRBhltFobNn1HsjEtD6DabeXTiR2B/iqlHXStCC9V46WEDV8xmvbzLzyiXzqPTKihw2HK3crCU738a5eN8vmttjYbcyrQawRDt35l2IYJrP9V/pDJa/RvNUDhQmzfi0gi7fSk90u/UQ+3ZB12rCAbiHVdTOxvidlXiELNJO+k8Xbsa/rNL2u2IorfFyt6385hVzzXQEbiiKEqBoh24oihKgdKiVSg7xg2N8qsvfSDKv3fATh+r7grGinYImxq3HPz0jpcg03R+rl/CTIfHeR9YmuKOpaXcTzqDWgUFBEqarvup7zoq80GC4qabzQ1WpzhD3ViK/d3dpdPLQtkMyk91aRVv8Bsnt7htzLg7yGVYgjYIRr64HWp8Gb8H17XEpdymPGRwrCa1zFC3k04xneptweOovZcPC/nxLl3OO3mRasR/dqwh8SqcKva7Zx1LnL97SjtLAdARuKIoSsGSypZqRwP4Hezv00EAM40x94tINwBPwf78JQBcYoz5LHtVbX5Umz14C69jL6ohEPSBXR2mss0UOwDMhZ0iCOCG8irfTFBTtnsBqGxzTSoqlAMAfmiMWSkinQCsEJGXYCcUi4wxU0VkCuzWtJMPcZ+8oajPUQCASbc8FZW1kyCKsasuBwD0mJ9dzxOBYABORmc5HAfMfizDIgBoDyvLPJCt9wggP+GutMXUEOcn33djVHSasXP8s6O5PPBzuTJcU+amuWXkmZI0jfRTTfZ99tPgtWgYrQCMAHAkbAcztaeIDETetV1+V5pqT3KqE/L5xjCngkrcFMrYWWGij0LInifs5+1PZhWKV02kPnWvLdtfIH3Z7kWIOe69Y1hd0q3GMSD5pb3aiXzHS1x6gN6z8vko23uJ3RT5m7QJ9RPit1Akr6hK9kcvdyl/XlwPF5e8KxWVuNjgrDVZw+qUOBWKV1NWxBxLpl4VijFmkzFmpcvvgv0W9QEwGmHL50eRvPOhkgLt5DB0lsMBAEXSBh1sw2gLlW2G6ATbwQAuHPDn0LabIWrKtghQ2eacBhkxRaQEwFdhHTN7GWM2AbaTF5Geh7i0yZGi8KqnzLPGjIuLgzHiD7tC9XvdYn/XDuaobgDwudmNXTb2cBWA4/JDtm7kO4RWlk3jw37kHTYoXna9zS+bflY4jzeUWeDSoWTYXDqITvDGKzacVsaUNZTtgN36JQ/bLo+GKbDUYJeyUWz9DQCAi/qFjabnlPAo0e8Gs4LKeOQaF9u7sQbL7XCG6DRlyysxfV3ZsO1HvDyToNnYdW73pnI6nPCza74m+GxPxMOuJKw3eGLG32xmEl1ycwX94zdIfpDKOBCYq/t2kv0bcbIl3/QSN5NKlNFxv76Cnx1PykZMESmGDWU2yRiT8jdJRCaIyHIRWb7f6cmUZA6YA1iNJTjBfmNT/t1g2QKFtL1brtkHt8hiY7ptV+VbF162nZG+bKvqv0CJJaUOXETawHbefzDG+OVQH4vYgBcu3RJ3rTFmpjFmiDFmSBva1UaxHDQHsRpL0BvHoKdEYVkbLFs7uFRq8wVsBzMIQLS9iso3I7BsI511GrItjjtFSYFUvFAEwG8ArDXGcFSc52HnFFNd+lxWapgpTjkhyt7R8/e1Dv/qZxdH+a6rluSkSsYY/A3L0RGd0E+O50NNKFs2HrkBVe/YExHpRroHFcqDD9otpK6vpF11h3OQIecffiMVvUGdY3XCZdjqw1tpNQQDK8ruAM4A8KI/kCdt16szyLf+pCDLyBA3Phh8t0y2kcF6riCZcFiC5T7DBt+4rdJ4ap/Osvmaso38ttOQbUeE+N0xKpSuLj73corAXxWWu484xT7ixQWjw/GhTq3y2Af0nGOj3C6nlvlJFK8bmPvdbwMALpx4frhkbNgaMFrDkGTEPJXyXj9I8fGjD7ECsXi//kQJFcYZNuNJRQf+DQCXA3hTRHwsuR/DfkBPi8hVAD4EcHEd1yt1sAOfYDM+RDG6YKmJduHuApVthtgIYDWs9+AMABgoIudB5ZsBasr2E6hsc48Yk7t9ZTpLN3O6nJ2z5wFA64F2ZDvhuReisgs62JHlwN/+W1RWcittzZFDmdRkoZm9wk4rG4bIUQaYkIEacMAo775XGooWhGyrwbsBAAd7Px6VbTHWTXAURVta1okMmlXuh6o3uSNu5lWDfjcUGsFnLLDSbWnJFsikfHmG44yX/b8XiminIvi9cweHorm/dqNEoWhWN5JhcprX1QcjZ0N2eEmfmTDmozq2CTo0Iv2M9TYEgnxKwgnjSgEAZ/0+NL7FsjscH+uCztFGN60mura5vGMopP2JMdulPLv0+bKXQlkJtdME77Tj4RG4nz2sjTm+MOY8IKxY5o3B/eyK3Trj266uxFQURSlQtANXFEUpUJp9MKt119qFMl5twvSt2Bf+aUK1SX5Q4tINVOam5o9RUUXIHhxp5/g9zGVRWc+33fSP923Fasq7KelmdssjI16kLin0GN818b7e/F4lNmHf+m2UX26n1We9/l5U9APc73KkNkmKT+2Nk7HOH3lKD0T+60/apOzSsHiz7K1SAMDLH59J1zwT5e574rsAgEmDHo7KDpb9DgBQXBWWsVat6xEun+u+79NJ63OdD2hXEsoSHLjKGWqLy0IRr7osckbSBMve3auIjKF8zTZekezRHXkURVGaPdqBK4qiFCjNUoVSfUEI5LPogl+6nC7ESI0rQra980Jhh5AKUn2MstPcfXtpDn+iW/ZeTnGYZ9NS73nOJ7yE4oUnjqAHkAdAs6SE8q6dzqWicopZPcP6hPfCq1HR4m+OtBlWUfH2apGOi7/a+a6O2oNo6f9Y661RtvSu6Oif7rWea5ftfjIqqxozPso/691H1pA6oq9VyVTdR4+ZSvn+TnVyHdfDe4xQDPCk9uj8u0uoaM0D9I9Xa3GwKtfv8MbeC9jjxH82vNbBL8+vf2GrjsAVRVEKlGY5Av/oG62j/DFFtUfePnBVm53BiNnSTZiR/+1QGjn7DYuoCMNJnjdb/+0d7Wk0PdieXDxma1S0Z2S45mBfd24ibuQCNCykaSHCwY+cv3B559plAHCSXU349KM0K6rwFmUOYMUy80bopJ1185xdCAGeXPugKK0XXLnIZsrL6ZrwzosP8wZPivrlZyg38+bI1JCjfYPDSB9d3X22s793CeWdcXEN9RbDyTjplzkmBcNy5y5gwyavBfCjffYd1x15FEVRmj3agSuKohQozVKFEsfPPwmbjy75dgkAwGx6s46zW14ZzasAAAN8SURBVCJuee9SmoYu9aqNBJ1HPqol19iU/VqdPbOqmHxukwI196mR0rObNd5YlaAyP5Xm6TWFz/aGr2oOBuZ3i6mgskKXXxuE93YGvnlxAZ3YGEuqqGqvjrs0lC10sb0p3ndSm1vg1VZ0n+0VLsMbasf5ZFM88IW0e4+v381Uj/buO1TN5/HnySEPGo6OwBVFUQqUZjkCP25KCAd73pRTY87YHFPW0vGGEx7N+bCZFGypPRkcEz5TQdfEBCNKMtwtcyk3vcbuCFMI+HfkwFJxu+OQ9a66zGVYfn7k2JxkVo3kvSXTpTymjA3EG2KO825QXs4cLvbTOvKHKvtpyFbHHM4gOgJXFEUpULQDVxRFKVByGg9cRLYC2I3kkD2FTndk9n36GWN61H9aMirblEhLtoDKNwVUtsnkpO3mtAMHABFZnm5Q/Xwkn94nn+qSCfLtffKtPo0ln94nn+qSCXL1PqpCURRFKVC0A1cURSlQmqIDn9kEz8wm+fQ++VSXTJBv75Nv9Wks+fQ++VSXTJCT98m5DlxRFEXJDKpCURRFKVBy2oGLyEgReVtE1ovIlFw+OxOIyNEi8j8islZE3hKRH7jybiLykoi869LDm6BuKtvs1U1lm936qXzTxRiTkz8ArQG8B+A4AG0BrAIwMFfPz9A7HAngVJfvBOAdAAMB3A1giiufAuCuHNdLZauyLTjZqnwb/5fLEfhpANYbY943xuyD3X96dA6f32iMMZuMMStdfhdsFPY+sO/xqDvtUQAX5rhqKtvsobLNLirfRpDLDrwPgI30fyWSY4oWFCJSAuCrAF4D0MsYswmwHyaSYoLmBJVt9lDZZheVbyPIZQcuMWUF6QIjIsUA5gCYZIypf+fR7KOyzR4q2+yi8m0EuezAKwEcTf/3BfBRDp+fEUSkDeyH9AdjzB9d8ccicqQ7fiSSI/TnApVt9lDZZheVbyPIZQf+OoABInKsiLQFMBbA8zl8fqMREQHwGwBrjTH30KHnAfidZ68A8FyOq6ayzR4q2+yi8m0MObbWngdroX0PwE1NbT1Oo/7DYKd3q2H3oH7DvdMRABbB7ge1CEC3JqibylZlW3CyVfk27k9XYiqKohQouhJTURSlQNEOXFEUpUDRDlxRFKVA0Q5cURSlQNEOXFEUpUDRDlxRFKVA0Q5cURSlQNEOXFEUpUD5fzMos30at5UQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                                   seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Guided saliency seems to give the best results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## grad-CAM - vanilla, guided, rectified"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These should contain more detail since they use `Conv` or `Pooling` features that contain more spatial detail which is lost in `Dense` layers. The only additional detail compared to saliency is the `penultimate_layer_idx`. This specifies the pre-layer whose gradients should be used. See this paper for technical details: https://arxiv.org/pdf/1610.02391v1.pdf\n",
    "\n",
    "By default, if `penultimate_layer_idx` is not defined, it searches for the nearest pre layer. For our architecture, that would be the `MaxPooling2D` layer after all the `Conv` layers. Lets look at all the visualizations like before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0tQzqLDb9FoOaj4J0SQdqui0GAz5KSqpV022ZybczMNY5tx7AObdeRMYUsU4lYfPnk1V6nvq7yHUyfEDSj1rYVhOXn/tuFB++xxY9w7CsFKbftO5hlkVeY9K+iO6+krQBs1zpu8RUhX+7PblQ9KzVXAfAsuk3m4ulcrr0hes27dsNrijt8UyLbU/7prpb/DjXlXIqR7eplHwQU0QuFZElIrJkJ22lvl2/QusW15z9BKNXmH5LR4Zu2023+ZJvA/6OiOwL4Lfvdnegc+5G51yDc66hln4Sqlc4OelX6xYZXdYKVjF5fbum35zIT7cDTbf5km8H4X5gDvB9v72vaDUqERuOSpIEaddJYM78JFPOAb/vM9dJoPj6TYsOIWVtufaUPMuabF3PtNzdaednW5S4N9EUvfuKC9dtXkvWBZR+s3XZU99ZjvRN1780uk1bUi2bTrItMNxDvHne9PQ+s/095EkuYYR3EGV1GCUiTcB/EL2gu0TkYuBN4JzCqtF/ed4tYhPN7KSNJ92DEE2LMf0Wg9bZ0DEf3AbYNhFMt8Vjx2zYNR/YAK0T8U2J6bbMZG3AnXOzu9l1SpHrUhJ2PDIFgIUzdLKqyAI/fOGcWHLQ5a/G5VLFfKdxqByb8f957u4Nzrn3KLZ+0yyBfKztbMflc062/fkOLg25I/P/W6U4us25Pln02+O5ZLfe+pJBnXTb1oDb1Vga3YYO88Qsx/XmO+zp/Hwt8XzeU4FWv83ENAzDqFKsATcMw6hSKrFzVjAD96uPy9+Z9lsA9lYDl0t9NOOU7yTOko5NfZIJoDTkM5jS2+uVk3y6w31Fd3HHaWRbhLdcVLp+g06zTYVPG5DszSBluP6wFFl398mmuxKnPjAL3DAMo0rZLS3w/e96Ky4fOajrb9TsR78EwAHLny1bncpKT4MxvbEecqV0IX/VTaHhf4VYZ8UYBO6JbOGixSSt/qVYZSht9mY2Sz9XuputnNZT6IVOzQI3DMOoUqwBNwzDqFJ2mw7tpjlJsqpvj+26QPGcxlNjyUHfiLLjlDPeu0/IddZkodcv5sBoPrG4lfQVl2LArxSDofm413qKs96R5X7FoLuBwFzJpseQNKw3Mz6zMaTTtnM5DJhmq1tTutgscMMwjCrFGnDDMIwqpZI6n3kxcEK0uOmJX10Uy9IWKF744rS4fMCm3TT6pCcK7VIHcs25nO+SarlGHKTFBGf7mvPJW14I+bg20p4rm36zLWmXjWz1DN38niIycswaUBDdPVM+327a0m3BddL6jhKm+S70Qhb6Ajv9dg8lmxpt6pVomioHuV64Ou0d6jzzCrPADcMwqpSqt8BXXTkJgN+P+0Pq/o89HyVECwOX0A8GL9PINjjYm5V4OpPNws5nQFKfMyRFlmu8dF/OIsym01zjs1tT9vfGkk+jkAFLfX7YpmXOLTa9aa3yGfgd5bcbxiay1rFdj+vu2uGao5Rsht8ep2RJPAVDjotWqxw1/D11mWh1sA51o+bvp9/SLHDDMIwqxRpwwzCMKqXqXShLz77Wl9KXaxv+5V0AtO9OyaoKIdsKJdkSBunu/Aa/bd+phKFcq2SqnDYwpwndUJ1QKHRJ9Tl6od8wzpS6Gk45Rte6oTeL7AbS9Mt2JQwPqQfKlH6Hddp2Jpyu6xEG0PQ5esA31EPHR8eUw3fiyfbtpsVa6+P0MzV1Og4gyrDBuH99LRZ9jPlxebvXeWMYmAQ6SBZDH+E/yjpaYlmNd9gOVe9wf5K1Bw7kZQDGkgycprlQPk06ZoEbhmFUKbksqTYJ+CUwDtgF3Oic+7GIjATuJAqEaQTOdc6ZmdsLWt12XuBZ2mhFECb4X3bTbbFYS7Q049t4W2UMmH6Lw1rg70h0uwUw3ZabXFwo7cDlzrllIlIHLBWRR4ALgUedc98XkbnAXOCK0lU1P3aOHQ5A7Y4JOZ/T0Rz1GV1bWyyTwYmLpmb0qK7njI76oasvH9TjtV1H0qWf+pUVzHDHs+e2QbS7nSzmUYg6dXPpK932JhNbXP5ACbf4re7i75MU07q7aXHMOi62wW91/KwOz13gty+lVfQHwJFAC7DPGBGZSV98u/m4qGJaVDl0xZVOtQtlRKctpL8z/Qmn6Ve7qJ7xWx2LvGEg8F9EYRYtwBT6TLcBrdvw/FrH2oXS6LfjEtGwrzUDsH7d/onwXHXOZL+9QMn0a1jlt+8r2aF+e0gicqqess4XkiCUhO7cjIqsLhTn3Hrn3DJfbvHVnADMAm71h91K924aoxsGDxjKXjXRX9JAqWUodQCDMN0WiX2JGm8g0u0H2LdbJPYFjvLlOnxrY7otM70axBSReqK/iEXAWOfceogaeREZU/TaFYEH7/5Fr8/58F+idZw3vLNXLNt7dGIFLTr69sIrBsz85mUA7PeNhXzgttESmT1bgf1KpttsM/g2KFnG4FlgaFIM1kt9oieG+bK2drQ1F+6p96fNkNQWZIihPSsZLB0wJMmetOu5PaPCfHXOEm+Vhudpa4RVDKWc367Wb+os0J2dtpCh37CIb72KRU6bQZhmtXd37/AXrxcI9nHJI89K8ujX1STf+xtveIv0YWXpP+y3jUMj3b60HVyJdaufOe370rK0wdyMSZWPRJu3D0su3+6f74nkqAVPJeUTgrV8jrrMnqocOukDu+5vHpNUpEVVqm5kVOnBHUlvv60mutAOdG9+I2nkPIgpIsOAe4CvOee2ZDtenXepiCwRkSU7act+Qj+k3bWzgoUcyBEQjTPkhNYtrrl0Fax2OrZC498CrM332zX9dkPQbe0k8tZtu+k2X3JqwEWklqjxvs05d68XvyMi+/r9+wLvpp3rnLvROdfgnGuo7SbUrz/jOjpYwULGMZkxEvvpe61bZHSZalxluJ1RA7P35yCx1Uy/xWCX0m3N3kHae90ONN3mSy5RKAL8N7DKOXeN2nU/0RD/9/32vpLUMAuzXvwcAI8ecnfRrvn0kXfkdNx2l3Tjd7quhvOZKy6My+8/13Xgc/yTO3llxV3sSR1T5AC9q/i6zbrIaxhFWaVkz/utHqT8VFL87HQAJl67OhaFGNcXmRnLmu+ZnJzzgN92k5wn7l02KNkZUazx7Cm/ikUn8ue4PPT0qH6LTj82lt3edj7OObZ86grY/yD48j/CqZeH3aX7drvVb4jzXa1ka+iKGjW7LHKnHHJFknxtf3/OKxwYy1Y9dVRyzjy/fU5dUrsOgmtK6Te4Ti6quTmWnciTcXnwlKjn/OcvfjSW/fzSi2mZ84+0neZ1++XYrVg63Wq3kI5Jb035djd7F9BmPZiuk1SFY5Nvu/WmswH49eV/G8suOPSeuPzEIccA8C9cHcsWvZN8c2NmR9cfpUYkt3uXWEs0BgNkxomH+O+OmiSefB1Rgr6WtuScaMyhK7n4wD8CfB54XkTCZ3El0Qu6S0QuBt4k0zNk5MCWTY28+9YyhjGcZ9wjQTwc021R6Hh6Mcz7FUw9FL54BMBMETkT02/BtD+1hLZf3ZvotukVTLflR5wr30yqvWSkO1ZOKcm1X/9esiKPy/KzVDcjGhDINhh58JMXJdd8c88u+/e7W42aLH6+y/58mOfuXuqca8h+ZCZS0+AY2p1ZS+5JnTIGxIIloSzwk5PRrxMej350Huz4ZCzba0E0IPfGSUm3+Dq+HpdvI+oxNf9RWeV6kNNffspHkpjAM3kIgPO5Lbn3omXJOc/FB8Z8e9I3ALhf9RiWyYl56RZABjQ4Bveg3zSyJvYKg8RqcPCSpDz759EA/O2rL072+6zJ285JvJ/XD/5qXP4Vnwdg1XJllWfoN/p7P2r/ZHTubKJEcOeT/D1Mv1+Z7avjA2O+PT3S70Ne6SsbLmXbkpfzmvYqezQ46nup29aUcrZVetIGfmco2TejzcfPeyAWTWJtXL71Ld8eXKbi+x5OinHYX72ShT8XfR/9BYbQTd1LCs4E3YtaKanfrs3ENAzDqFKsATcMw6hSqj6ZVWDqlQt7fc5ZHN3zNVmRb3UqFz27S3fIopB0DpqVuCbq/XQ1PehyajxKBn//u18DsP3zyWVWbIu2h308CQ279vIr4/KVZ34PgMbT62PZCNXHn7Yx6kuK7lH7a7JOyZaqcvD0qNluRGniMwaPyoLW7xGq7BMlTTkvcQ3N5EUA9lGDXmdzf1w+52dRV/71LyWXCcOep/04GTT/l29cF5e/8jc3ROccXh/LtH6nrPPvRcU3xzMHdbyI7r4H/Z+UiNp8RNkGP6WzvZRNSbi0mjWpc2qPvuJNAC7hpljW4EfJa1T2/+1qdnBIFDWCZJZ/cJfoQcgwoAgwaUK0/6HfnZm6P/ydjFWKDLL6eOpnUjd9z8eP/lgsu3raVVHh18kzspJUzAI3DMOoUqwBNwzDqFJ2GxeKkSN6avEJSfHcWVH6ijvXXZgIQ9T/K+qc15PiAt+tm6d2h0n1dY8lsqlqAu7oW6LIndHvJ31Cp9wli/2MYR29e1hwRagoE5WSGT7h6/ORJPLiTs4DYPWDh1N0esrjrV0oSr9nnfdbAO59P4nzrg361aH3Kkx8gXdjpOn3IKWziTeo/fdHUUCHv68upNwhK3xQhdbv9BDKfLoSavdPFO7Pww2JDyVEuzTd5ndu1FcsAmlL6qnp/8MuS1x0jxO5Hw4+MsnjfY1/Zj01VKezC7E+OkAnRGLr/FQfOiSZwv6hhuib/c7UJA484wZv+q2OhgkX08+j3VPe23LaVxbEopn/HrnWbrr6klj2hC2pZhiGsXthFnh/RlkFG7yp0Dw+MdFHT/Jx7jpJkMqrdIK30pShmaTcPEjJxtOVN5OiqGOPDUaUXkvWTwVZ/YnEBFuiBqCfJ0pI9HuV+G7VDd4an59y70IJesu28K+yxDb7KZDrhifx8VMmNXc5TuvqBG8ZZ9XvJFUOY3Z6wFdZ64eFHpROMeX1u/wj02PRUjXC/bzPiXo3n4llTT/wx4buQUYStCKQtviz+l7bWpO0HG17+rLK1BH6A9pA1vOJW1JkoaxVM1EP7IaekuqFZqSODWOfespI6D3ov4FDVTmcP50u6AHW7jAL3DAMo0qxBtwwDKNKMRdKf0O7Q9Q04McGngXAmE8nMd+j/yHyc+iu3FDV6Rzs0wPrWNs2n8N4M3F2OjZ3JMm9d7T6HMdJDiCGXZjcM8TNfqDyYje95X0Ef1QjhHrqcUhspFfkCWOkxe7aa9Kmymt3yPykuODfTgOg/qykTz7yoiiJlM69PUilXB5MlCxN6zfkiN6kEqZv3ZbEum/fGumtZlpyTt3ZSr/+XtuVfptf9fq9T82ET9Ovzr21stM+7YsoNkHPjYlo53VJDvrTvhWldPjiMz+LZcf6nAMHkq7bqf5iE9apPNs+3t2pUcy3Rw6PyyHm+13lZNHvIbjJ1pKkiXjR+7rWZvi5EsI71vubnvL+lIwVps5PPd8scMMwjCrFLPD+QnjT2mpMs1hVuFLzwMkZWyBzpZxxnbaQDNpoS1RbwW93lW1tHd1ld9V+mfq5V6aUf5SINvrAto1pazlColediThH/e5S8XEbWxNrdWOp9NqR/ZC8Cd+sTiGrYis3vh3p8eojrkqEYbxbh3WqMMQpB0cf/xHj/xLLxrMegBr1R6J7ksFKfpVkzcymV9VCoit9D0aHCYZyo5Klrc6U53sxC9wwDKNKsQbcMAyjSilrPnARaSYaKijl0FK5GUVxn2eKc67Xa0yZbnMiL92C6TcHTLeZlOXbLWsDDiAiS/JNql+JVNLzVFJdikGlPU+l1adQKul5KqkuxaBcz2MuFMMwjCrFGnDDMIwqpS8a8Bv74J6lpJKep5LqUgwq7XkqrT6FUknPU0l1KQZleZ6y+8ANwzCM4mAuFMMwjCqlrA24iJwhIi+LyBoRmVvOexcDEZkkIo+LyCoReUFE/sHLR4rIIyKy2m/3znatEtTNdFu6upluS1s/02++OOfK8o9owYtXgf2AQcByYGa57l+kZ9gXOMqX64jWqpkJ/BCY6+VzgR+UuV6mW9Nt1enW9Fv4v3Ja4McAa5xzrznndgC/AWaV8f4F45xb75xb5sstRCneJxA9x63+sFtBrSxQHky3pcN0W1pMvwVQzgZ8ArBW/b+JzGXqqgoRqQeOBBYBY5dyquIAAAESSURBVJ1z6yF6mWQu6lEOTLelw3RbWky/BVDOBlxSZFUZAiMiw4B7gK8557ZkO74MmG5Lh+m2tJh+C6CcDXgTmav3TSRz5b6qQERqiV7Sbc65e734HRHZ1+/fl3it6bJhui0dptvSYvotgHI24M8C00VkqogMAj4L3F/G+xeMiAjw38Aq59w1atf9wBxfngPcV+aqmW5Lh+m2tJh+C6HMo7VnEo3Qvgr8a1+PHudR/xOIuncriFK1P+efaR/gUWC1347sg7qZbk23Vadb029h/2wmpmEYRpViMzENwzCqFGvADcMwqhRrwA3DMKoUa8ANwzCqFGvADcMwqhRrwA3DMKoUa8ANwzCqFGvADcMwqpT/D/3plHRQMz84AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gZmYl5QJuZlZSXkJpkq2rXwBgzrRDsr5xLGrVcMxsEPAM3MyspFzAzcxKygXczKykXMDNzEqq0OuBS1oFrANWF7bT/E2guc/nwIjYu78bOdua1JUtON8aONvtFfLaLbSAA0h6sN6L6rejdno+7TSWZmi359Nu42lUOz2fdhpLMxT1fLyEYmZWUi7gZmYl1YoCPqcF+8xTOz2fdhpLM7Tb82m38TSqnZ5PO42lGQp5PoWvgZuZWXN4CcXMrKQKLeCSTpf0O0lPSppd5L6bQdL+kv5XUqekxyR9MO0fL+kuSU+k38e1YGzONr+xOdt8x+d86xURhXwBQ4FlwCHACOBR4Mii9t+k5zAZOD5tdwBLgSOBfwVmp/2zgesKHpezdbaly9b5Nv5V5Az8RODJiHgqIl4FvgecXeD+GxYRXRHxcNruBjqBKSTPY256t7nAOQUPzdnmx9nmy/k2oMgCPgVYXvHzirSvlCQdBBwHLAb2iYguSH6ZwMSCh+Ns8+Ns8+V8G1BkAddO+kp5CIykMcAC4MqIeLnV48HZ5snZ5sv5NqDIAr4C2L/i5/2A5wrcf1NIGk7yS/pORNyWdj8vaXJ6+2RgZcHDcrb5cbb5cr4NKLKAPwBMlXSwpBHABcDCAvffMEkCvg50RsT1FTctBC5K2xcBdxQ8NGebH2ebL+fbiILfrT2D5B3aZcA/tfrd4zrG/yaS/94tAX6dfp0B7AXcAzyRfh/fgrE5W2dbumydb2NfPhPTzKykfCammVlJuYCbmZWUC7iZWUm5gJuZlZQLuJlZSbmAm5mVlAu4mVlJuYCbmZXU/wMYWGsin5Kz7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_cam\n",
    "\n",
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_cam(model, layer_idx, filter_indices=class_idx, \n",
    "                              seed_input=x_test[idx], backprop_modifier=modifier)        \n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case it appears that saliency is better than grad-CAM as penultimate `MaxPooling2D` layer has `(12, 12)` spatial resolution which is relatively large as compared to input of `(28, 28)`. Is is likely that the conv layer hasnt captured enough high level information and most of that is likely within `dense_4` layer. \n",
    "\n",
    "Here is the model summary for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 24, 24, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 9216)              0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 128)               1179776   \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "preds (Dense)                (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 1,199,882\n",
      "Trainable params: 1,199,882\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization without swapping softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As alluded at the beginning of the tutorial, we want to compare and see what happens if we didnt swap out softmax for linear activation. Lets try this with guided saliency which gave us the best results so far."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Swap linear back with softmax\n",
    "model.layers[layer_idx].activation = activations.softmax\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "    \n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                               seed_input=x_test[idx], backprop_modifier='guided')\n",
    "\n",
    "    f, ax = plt.subplots(1, 2)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    ax[1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not work as well! \n",
    "\n",
    "It does not work! The reason is that maximizing an output node can be done by minimizing other outputs. Softmax is weird that way. It is the only activation that depends on other node output(s) in the layer."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
